A140962 Negative values of the inverse binomial transform of A045883.

0, -1, -1, -3, -1, -7, 3, -19, 23, -63, 107, -235, 447, -919, 1811, -3651, 7271, -14575, 29115, -58267, 116495, -233031, 466019, -932083, 1864119, -3728287, 7456523, -14913099, 29826143, -59652343, 119304627, -238609315, 477218567, -954437199

Offset: 0

Author

Paul Curtz, Jul 27 2008

Keywords

• easy
• sign

Comments

The inverse binomial transform of A045883 is 0,1,1,3,1,7,...

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,3,-2).

Programs

Magma

[-(1/9)-(2/3)*n+(1/9)*(-2)^n: n in [0..40]]; // Vincenzo Librandi, Aug 08 2011

Mathematica

LinearRecurrence[{0,3,-2},{0,-1,-1},50] (* Paolo Xausa, Nov 14 2023 *)

Formula

a(n+1) - a(n) = (-1)^(n+1)*A078008(n).

a(n+1) - a(n) = 2*(-1)^n*A001045(n-1), n > 0.

a(n) = 3*a(n-2) - 2*a(n-3).

G.f.: -x*(1+x)/((1+2*x)*(1-x)^2). - R. J. Mathar, Nov 11 2008

Extensions

Edited and extended by R. J. Mathar, Nov 11 2008